{"id":"https://openalex.org/W2127140420","doi":"https://doi.org/10.1007/s10957-012-0069-7","title":"Beyond Canonical DC-Optimization: The Single Reverse Polar Problem","display_name":"Beyond Canonical DC-Optimization: The Single Reverse Polar Problem","publication_year":2012,"publication_date":"2012-05-09","ids":{"openalex":"https://openalex.org/W2127140420","doi":"https://doi.org/10.1007/s10957-012-0069-7","mag":"2127140420"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-012-0069-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-012-0069-7","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11568/188948","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007636174","display_name":"Giancarlo Bigi","orcid":"https://orcid.org/0000-0002-0964-3294"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]},{"id":"https://openalex.org/I4210160382","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Pisa","ror":"https://ror.org/05symbg58","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210160382"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giancarlo Bigi","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo B.Pontecorvo, 3, 56127, Pisa, Italy","Dipartimento di Inform\u00e1tica, Universit\u00e1 di Pisa, Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo B.Pontecorvo, 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I4210160382","https://openalex.org/I108290504"]},{"raw_affiliation_string":"Dipartimento di Inform\u00e1tica, Universit\u00e1 di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061303343","display_name":"Antonio Frangioni","orcid":"https://orcid.org/0000-0002-5704-3170"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]},{"id":"https://openalex.org/I4210160382","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Pisa","ror":"https://ror.org/05symbg58","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210160382"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Antonio Frangioni","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo B.Pontecorvo, 3, 56127, Pisa, Italy","Dipartimento di Inform\u00e1tica, Universit\u00e1 di Pisa, Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo B.Pontecorvo, 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I4210160382","https://openalex.org/I108290504"]},{"raw_affiliation_string":"Dipartimento di Inform\u00e1tica, Universit\u00e1 di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100327280","display_name":"Qinghua Zhang","orcid":"https://orcid.org/0000-0003-0582-3834"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]},{"id":"https://openalex.org/I4210121573","display_name":"Wuchang University of Technology","ror":"https://ror.org/02mqsna37","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210121573"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinghua Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuchang, Luojia Hill, 430072, Wuhan, China","School of Mathematics, and Statistics, Wuhan University, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuchang, Luojia Hill, 430072, Wuhan, China","institution_ids":["https://openalex.org/I37461747","https://openalex.org/I4210121573"]},{"raw_affiliation_string":"School of Mathematics, and Statistics, Wuhan University, Wuhan, China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5007636174"],"corresponding_institution_ids":["https://openalex.org/I108290504","https://openalex.org/I4210160382"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.17819383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"155","issue":"2","first_page":"430","last_page":"452"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7131156325340271},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6969097852706909},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.631784200668335},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5962550044059753},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5691671371459961},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5145953893661499},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.48815566301345825},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.4770714044570923},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.44561058282852173},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4365558922290802},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.433609277009964},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.42531198263168335},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4183153510093689},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.41448935866355896},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.301312655210495},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23673570156097412},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11276569962501526},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09297934174537659}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7131156325340271},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6969097852706909},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.631784200668335},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5962550044059753},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5691671371459961},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5145953893661499},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.48815566301345825},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4770714044570923},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.44561058282852173},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4365558922290802},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.433609277009964},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.42531198263168335},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4183153510093689},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.41448935866355896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.301312655210495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23673570156097412},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11276569962501526},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09297934174537659},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-012-0069-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-012-0069-7","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0069-7","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-012-0069-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:arpi.unipi.it:11568/188948","is_oa":true,"landing_page_url":"http://hdl.handle.net/11568/188948","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arpi.unipi.it:11568/188948","is_oa":true,"landing_page_url":"http://hdl.handle.net/11568/188948","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W44939114","https://openalex.org/W46129499","https://openalex.org/W75157487","https://openalex.org/W642137701","https://openalex.org/W1897767665","https://openalex.org/W1969423031","https://openalex.org/W1971867305","https://openalex.org/W1982405519","https://openalex.org/W1988746686","https://openalex.org/W2016408076","https://openalex.org/W2018753153","https://openalex.org/W2028042462","https://openalex.org/W2044800863","https://openalex.org/W2061405998","https://openalex.org/W2064451830","https://openalex.org/W2080893543","https://openalex.org/W2082476243","https://openalex.org/W2131524354","https://openalex.org/W2141286079","https://openalex.org/W2147656689","https://openalex.org/W2610216665","https://openalex.org/W3150183338","https://openalex.org/W4246092883","https://openalex.org/W4300819821"],"related_works":["https://openalex.org/W2073713056","https://openalex.org/W3110702597","https://openalex.org/W2125620709","https://openalex.org/W2110441383","https://openalex.org/W2045932760","https://openalex.org/W4233149903","https://openalex.org/W2326878701","https://openalex.org/W4293864700","https://openalex.org/W2032550399","https://openalex.org/W2057791178"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
